Variance Estimation in the Presence of Imputation for Missing Data

Item nonresponse is usually treated by some form of deterministic or random imputation. We focus on deterministic imputation; in particular, ratio and nearest neighbour imputations commonly used in establishment surveys. Frequentist inference from imputed data is based on a repeated sampling framework and assumed response mechanism. On the other hand, use of imputation models requires only that the assumed model holds for the respondents. Treating the imputed values as true values and computing standard errors using standard formulae applicable to complete samples can lead to serious underestimation of true standard errors, especially when the item nonresponse is appreciable. This paper reviews some recent work on variance estimation under single imputation that takes proper account of the additional variability due to the unknown missing value; in particular, work on jackknife, jackknife linearization and modified balanced repeated replication.